Laser spectral engineering for lithographic process

ABSTRACT

An integrated circuit lithography technique called spectral engineering by Applicants, for bandwidth control of an electric discharge laser. In a preferred process, a computer model is used to model lithographic parameters to determine a desired laser spectrum needed to produce a desired lithographic result. A fast responding tuning mechanism is then used to adjust center wavelength of laser pulses in a burst of pulses to achieve an integrated spectrum for the burst of pulses approximating the desired laser spectrum. The laser beam bandwidth is controlled to produce an effective beam spectrum having at least two spectral peaks in order to produce improved pattern resolution in photo resist film. Line narrowing equipment is provided having at least one piezoelectric drive and a fast bandwidth detection control system having a time response of less than about 2.0 millisecond. In a preferred embodiment, a wavelength tuning mirror is dithered at dither rates of more than 500 dithers per second in phase with the repetition rate of the laser. In one case, the piezoelectric drive was driven with a square wave signal and in a second case it was driven with a sine wave signal. In another embodiment, the maximum displacement was matched on a one-to-one basis with the laser pulses in order to produce a desired average spectrum with two peaks for a series of laser pulses. Other preferred embodiments utilize three separate wavelength tuning positions producing a spectrum with three separate peaks.

FIELD OF THE INVENTION

This application is a continuation-in-part of Ser. No. 09/918,773, filedJul. 27, 2001, Ser. No. 09/608,543 filed Jun. 30, 2000 and Ser. No.09/854,097 filed May 11, 2001, 09/597,812 filed Jun. 19, 2000, which wasa continuation-in-part of Ser. No. 08/898,630 filed Jul. 22, 1997 nowU.S. Pat. No. 6,078,599 and Ser. No. 09/501,160 filed Feb. 9, 2000. Thisinvention relates to lasers and, in particular, to techniques forcontrol of the bandwidth of the output beam.

BACKGROUND OF THE INVENTION Wavelength Control

Lasers are used for many applications. For example, lasers, such as KrFand ArF excimer lasers, are used in stepper and scanner equipment forselectively exposing photoresist in a semiconductor wafer fabricationprocess. In such fabrication processes, the optics in the steppers andscanners are designed for a particular wavelength of the laser. Thelaser wavelength may drift over time and, thus, a feedback network istypically employed to detect the wavelength of the laser and correct thewavelength as necessary.

In one type of feedback network used to detect and adjust the wavelengthof a laser, an etalon receives a portion of the emitted light from thelaser. The etalon creates an interference pattern having concentricbands of dark and light levels due to destructive and constructiveinterference by the laser light. The concentric bands surround a centerbright portion. The diameter of a light band produced by an etalon isused to determine the wavelength of the laser to a fine degree, such asto within 0.01-0.03 pm. The width of a light band is used to determinethe spectral width of the laser output. The interference pattern isusually referred to as a fringe pattern. A grating spectrometer is alsoused in prior art devices to measure wavelength to a relatively coursedegree. The fringe pattern and the grating signal may be opticallydetected by a sensitive photodetector array. A detailed description of aprior art wavemeter is disclosed in U.S. Pat. No. 5,978,394 which isincorporated herein by reference.

Various methods are well known for wavelength tuning of lasers.Typically the tuning takes place in a quickly replaceable modular devicereferred to as a line narrowing module or line narrowing package (LNP).A typical technique used for line narrowing and tuning of excimer lasersis to provide a window at the back of the discharge chamber throughwhich a portion of the laser beam passes into the LNP. There, theportion of the beam is expanded in a beam expander and directed to agrating which reflects a narrow selected portion of the laser's naturalbroader spectrum back into the discharge chamber where it is amplified.The laser is typically tuned by changing the angle at which the beamilluminates the grating. This may be done by adjusting the position ofthe grating or providing a mirror adjustment with a pivoting mirror inthe beam path. The adjustment of the grating position or the mirrorposition may be made by a mechanism which we will refer to as a laserwavelength adjustment mechanism.

In the prior art, the typical feedback network is configured to maintainthe nominal wavelength within a desired range of wavelengths. Typicalspecifications may establish this range at values such as ∀0.05 pm of atarget wavelength such as, for example, 248,327.1 pm, for a KrF laser asapplied to the average of the wavelengths of a series of pulses referredto as “pulse window”. A typical pulse window would be 30 pulses. Anothertypical specification is the standard deviation of the measuredwavelength values for a series of pulses (such as 30 pulses). This valueis referred to as wavelength sigma, Φ, and is calculated using astandard formula for standard deviations. Also, sometime specificationsare in terms of 3Φ which is merely three times the measured standarddeviation. A typical 3Φ specification may be 0.15 pm.

The limitations of acceptable optical lens materials to fused silica andcalcium fluoride for use with deep ultraviolet light at 248 nm and 193nm wavelengths have meant that projection lenses for KrF and ArFlithography, to a large degree, cannot be corrected for wavelengthvariations. Chromatic aberrations emerge since the index of refractionof any optical material changes with wavelength, and hence, the imagingbehavior of a lens also varies with wavelength.

The detrimental effects of chromatic aberrations for an uncorrected lenscan be mitigated by using a light source with a very narrow range ofwavelengths. Spectral line-narrowed excimer lasers have served thispurpose for deep-UV lithography. In the past, laser specifications haverequired the FWHM bandwidth to be smaller than a specified value such as0.5 pm but with no lower limit on bandwidth. Specifications are alsodirected at the 95 percent integral bandwidth. A typical 95% Ispecification would be less than 1.2 ppm. However, recently integratedcircuit manufacturers have noticed that the quality of their integratedcircuits can be adversely affected by bandwidths, such as about 0.35 pmFWHM, which are substantially narrower than the bandwidths for whichtheir optical systems were designed.

A lithography technique, called FLEX (short for, “focus latitudeenhancement exposure”) has been shown (through simulation andexperiment) to improve the depth of focus by utilizing multiple exposurepasses of the same field with different focus settings. This techniqueis also commonly referred to as focus drilling, since the physicalthickness of the photoresist film is exposed in multiple passes atincremental focus settings. The image in photoresist is formed by thecomposite of the multiple exposure passes.

Several difficulties result from this FLEX process with both step andscan as well as step and repeat exposure implementations. Multiple passexposure results in additional overlay (image placement) errors andimage blurring. This has further implications on process latitude, focusrepeatability as well as wafer throughput since multiple exposuresrequire multiple imaging passes.

What is needed is a better technique for providing improved qualityintegrated circuit lithographic exposures.

SUMMARY OF THE INVENTION

The present invention provides an integrated circuit lithographytechnique called spectral engineering by Applicants, for bandwidthcontrol of an electric discharge laser. In a preferred process, acomputer model is used to model lithographic parameters to determine adesired laser spectrum needed to produce a desired lithographic result.A fast responding tuning mechanism is then used to adjust centerwavelength of laser pulses in a burst of pulses to achieve an integratedspectrum for the burst of pulses approximating the desired laserspectrum. The laser beam bandwidth is controlled to produce an effectivebeam spectrum having at least two spectral peaks in order to produceimproved pattern resolution in photo resist film. Line narrowingequipment is provided having at least one piezoelectric drive and a fastbandwidth detection control system having a time response of less thanabout 2.0 millisecond. In a preferred embodiment, a wavelength tuningmirror is dithered at dither rates of more than 500 dithers per secondin phase with the repetition rate of the laser. In one case, thepiezoelectric drive was driven with a square wave signal and in a secondcase it was driven with a sine wave signal. In another embodiment, themaximum displacement was matched on a one-to-one basis with the laserpulses in order to produce a desired average spectrum with two peaks fora series of laser pulses. Other preferred embodiments utilize threeseparate wavelength tuning positions producing a spectrum with threeseparate peaks. In another preferred embodiment, effective bandwidths inthe range of 0.4 pm to 2.0 pm are produced in a series of pulses (suchas a 30-pulse window of pulses).

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a graph showing the variation of best focus with wavelength.

FIG. 1B shows typical narrow band gas discharge laser spectra.

FIGS. 2A-I demonstrate features of a preferred embodiment of the presentinvention.

FIG. 3 shows the variation of aerial image intensity with bandwidth.

FIGS. 4A, 4B and 4C shows variation of the change in critical dimensionwith bandwidth.

FIG. 5 is a drawing of a narrow band laser system.

FIG. 5A and B show features of a tuning mechanism.

FIG. 6 is a drawing of a wavemeter.

FIGS. 6A-D show how wavelength and bandwidth is calculated.

FIGS. 6E-H show features and details of preferred etalons.

FIG. 7 show electronics and processors used in a preferred wavelengthcontrol system.

FIGS. 8A, 8B1 and 8B2 show features of a wavelength control system withPZT drive.

FIG. 8C shows the effect of PZT control.

FIGS. 8D and E show control algorithms.

FIGS. 9A-D show the wavelength effects of two different PZT inputpatterns.

FIGS. 10A-I show various techniques for creating effective bandwidthpatterns.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS Simulation

Simulation of the effects of wavelength and bandwidth changes have beenperformed by Applicants. The main effect of changing the exposurewavelength for a non-chromatic corrected lens is a change in theposition of the focal plane. Over a fairly wide range of wavelengths,this change in focus is approximately linear with the change in thenominal wavelength (i.e., the central wavelength of the illuminationspectrum). The wavelength response of a lens can be determinedexperimentally by manually changing the central wavelength of the laserand using the imaging sensor of the stepper to monitor the shift infocus that results. FIG. 1A shows an example of such a measurement.

Given the change in focus with change in wavelength, the use of abroadband illumination spectrum means that each wavelength in thespectrum will produce an aerial image with a different best focus. Thetotal aerial image will be a sum of the aerial images at each focalposition, weighted by the relative intensity of each wavelength in theillumination spectrum. This technique is based on multiple focal planeexposures. Latest versions of a computer program PROLITH/2 (availablefrom KLA Tencor with offices in Austin, Tex.,) incorporate these typesof effects. Actual laser spectra measured on a variety of commerciallyavailable lasers were used in this work to represent laser spectra. FIG.1B illustrates three examples of KrF laser spectra.

In order to understand the impact of laser bandwidth on the lithographicprocess in the presence of chromatic aberrations, Applicants startedfrom investigation of the aerial image of a 180 nm isolated line. FIG. 3shows how changing bandwidth affects the aerial image under a specificset of conditions. (The image dimension is usually assumed to correspondto the 0.3 image intensity values.) For these simulations the followinginput parameters were used: NA=0.6, Φ=0.75, 8₀=248.3271 nm. Laserspectra with 0.5 pm, 1.2 pm, 2.1 pm bandwidths at FWHM and amonochromatic light source were used in this simulation study, and achromatic aberration focus response of 0.225Φm/pm was assumed. As can beseen in FIG. 3, changes in the bandwidth causes noticeable changes inthe image intensity distribution.

The impact of laser bandwidths on critical dimensions (CD) variations ofisolated lines with different sizes was evaluated using an aerial imagethreshold model. In this study the following lithography input parametersettings were used: Φ=0.75, 8₀=248.3271 nm, aerial image threshold at30%, NA=0.6, 0.7, and 0.8. The simulations were performed for isolatedlines ranging from 240 nm to 140 mn. The chromatic aberration responsewas assumed at 0.225Φm/pm. As shown in FIGS. 4A, 4B and 4C, changes inthe bandwidth (either increases or decreases) can result in substantialchanges in the critical dimensions of the integrated circuit linesespecially at higher numerical aperture values. As shown in FIGS. 4A-4Cthe smallest bandwidth (i.e., 0.35 pm) produces the smallest change inthe critical dimension as a function of mask dimension. A reader mightconclude from this data that lithography systems should be designed forthe smallest possible bandwidth. The problem with that approach is thatmaintaining the bandwidth consistently at 0.35 pm over the life of thelight source would be very difficult and expensive with today'stechnology. Therefore, the normal practice is to design lithographysystems for best performance at a bandwidth which is somewhat largerthan the smallest possible bandwidth, such as about 0.5 pm. But if alithography system is designed for best performance at 0.5 pm, an“improvement” in the laser bandwidth down to 0.35 pm will often lead toa worsening of critical dimensions and decreased quality of theintegrated circuit.

Dither Tuning Mirror to Simulate Desired Wavelength

The wavelength and bandwidth monitoring equipment and the wavelengthtuning equipment described in detail below permit bandwidth control ofthe laser beam. In a first embodiment the tuning mirror is dithered at adesired frequency and amplitude to basically widen a too narrowbandwidth to an effective bandwidth having a desired value.

The technique involves monitoring the bandwidth with wavemeter 104 shownin FIG. 5 and FIG. 6. If the bandwidth is less than the desiredbandwidth the wavelength control equipment is utilized to dither mirror14 shown in FIG. 5 at frequent intervals to cause very slight shifts inthe spectrum on a pulse to pulse basis so that the average integratedspectrum over a window of pulses simulates approximately a constantspectrum with bandwidth approximating the desired bandwidth.

For example, if the optical equipment for a scanner is designed for abandwidth of 0.4 pm and because of a decrease in the fluorineconcentration the bandwidth of individual pulses is 0.3 pm, mirror 14may be dithered about its nominal position to produce plus and minusshifts in the nominal wavelength of about 0.05 pm in order to maintainthe same nominal wavelength with the effective increase by 0.1 pm. For atypical commercial excimer laser of the type discussed above, a changein the pivot position of mirror 14 of about 2 nm is required to producea 0.05 pm shift in the wavelength. This change in mirror position iseasily provided by the piezoelectric drivers referred to above and shownin FIG. 5A as item 80. Typically in the integrated circuit fabricationeach spot on the wafer is illuminated with a number of pulses usually inthe range of about 30 to 150 pulses so that the dither rate should besufficient so that each die spot receives about equal portions of pulsesfrom both sides of the dither.

Thus, if the number of pulses illuminating a spot is 30 the dither rateshould be at least about ¼ the pulse rate. So if the pulse rate is 2000Hz the dither rate preferably would be at least 500 Hz. This is noproblem for the equipment and software referred to above.

Spectral Engineering

FIG. 2A shows the variation of focus with centerline wavelength for amodem 0.6 NA stepper type lithography using a line narrowed KrF lightsource having a FWHM bandwidth of about 0.35 pm. FIG. 2A also include aplot of the laser spectrum plotted as normalized intensity versusdeviation from the centerline wavelength. The focus versus centerlinewavelength slope for this system is −0.23 Φm/pm.

Applicants have shown that substantial improvements in lithographicimaging can be provided using a spectral engineering techniquesdeveloped by Applicants. Applicants refer to this technique as RELAXwhich is an acronym for Resolution Enhancement by Laser-SpectrumAdjusted Exposure. In these techniques, the wafer is illuminated withtwo or more specific narrowband centerline wavelength during a singleillumination period. This produces results which are improved over thedither technique referred to above. The results are similar to the FLEXtechnique discussed in the background section of this specification butconstitutes a major improvement over FLEX since Applicants' techniqueinvolves only one positioning of the lithography equipment. Therefore,errors associated with adjustments of this equipment are avoided.

Dual Mode Illumination

The results of simulations performed by Applicants show proof of conceptfor use of a dual-mode illumination spectrum to improve resolution inphoto resist film. In this dual mode simulation work, Applicantssimulated the process parameters for 200 nm isolated, semi-dense (1:2)and dense (1:1) contact hole patterns. A binary (chrome on glass)reticle pattern and conventional illumination (e.g., a stepper systemwith a numerical aperture, NA of 0.7 and a 0.75 sigma) at KrF exposurecentral wavelengths, (8_(≅),=248.385 nm) were modeled in the simulation.The photo resist was modeled as UV6, 5200A casting thickness on AR2bottom anti-reflective coating in order to quantify the obtainedresolution enhancement of the imaged pattern. The double-mode spectrumused as the simulation input is shown in FIG. 2B. In this case, thespectrum is generated by summation of a single mode (nominal) spectrum(bandwidth: FWHM=0.45 pm, E95%=1.86 pm) and its copy with a 4 pmwavelength offset. If S(8) represents the spectral density function ofthe nominal (0.45 pm/1.86 pm FWHM/E95%) spectrum, the spectral densityof the double-peak RELAX spectrum [S_(RELAX)(8)] can be expressed asS_(RELAX)(8)=S(8)+S(8+4 pm). Technologies for actual generation of suchspectral properties are discussed in the following section. Thelongitudinal focus plane to centerline wavelength slope used for thismodel is −0.225 :m/pm which is shown in FIG. 2A.

The results of this simulation of the double-peak RELAX technique arecompared in FIG. 2C with similar simulations of a monochromatic beam anda conventional single peak spectrum with FWHM bandwidth of 0.45 pm and a95% integral bandwidth of 1.86 pm. The critical dimension response tofocus and dose are presented for 1:1 dense contact holes for threeillumination spectral distributions; (1) monochromatic illumination, (2)conventional laser spectrum and (3) the 4 pm double mode RELAXillumination with a spectrum as shown in FIG. 2B (i.e., two 0.45 pm FWHMspectral bands with centerlines separated by 4.0 pm).

FIG. 2D presents plots of the resist feature widths of holes which havea target diameter of 200 nm as a function of depth of the holes. Thefigures are plotted for several doses ranging from 17 J/cm² to 26 J/cm²in the monochromatic example and from 25 J/cm² to 32 J/cm² in the RELAXexample. This ordinant is feature width and the absissa is labeled focusbut actually represents the depth of the feature in microns with zerotaken as the focal plane of the centerline wavelength. An “ideal” graphwould be a straight line at 200 nm over a depth of at least 1.0 micron,with insignificant variation in width with exposure dose. The FIG. 1Dplots reveal that the RELAX simulation produces a set of plots muchcloser to the “ideal” graph than either the conventional ormonochromatic example.

FIG. 2D is another set of graphs made from the same data as was used forthe FIG. 2C plots. In this case, Applicants selected the plot for eachof the examples and plotted for that exposure the exposure latitude(i.e., the percent of the dose can vary without causing the criticaldimension to vary more than 10% from a target value) as a function ofthe depth of a hole having a target width of 200 nm. Again, these threegraphs show a great improvement in performance resulting from the use ofthe RELAX techniques.

The dramatic improvement in the depth for which the critical dimensioncan be controlled to within 10% with the RELAX approach is apparent. Theimprovement in depth of focus is larger than fourfold at the 5% exposurelatitude level compared to the monochromatic and conventional resultsfor dense contacts. Some exposure latitude loss is observed by using thedouble-mode spectrum. This loss in exposure latitude is most pronouncednear best focus (i.e., 0.0 depth of focus). As compared with theconventional spectrum example, the slight increase in the target dose(from about 25 mJ/cm² to about 29 mJ/cm²) for the RELAX case as comparedto the conventional example should be noted.

The simulation results for the other pattern configurations referred toabove were tested with the result that the two-peak RELAX techniqueproduced better pattern resolution as compared to both monochromatic andthe conventional spectrum for every example tested. Therefore, weconclude that the RELAX application (using a dual-mode spectrum with 4pm mode separation) for focus drilling provides dramatic improvement inthe overall process window area. A tradeoff is realized between depth offocus improvement and loss of exposure latitude, however, the DOFincreases at a higher rate than the reduction of exposure latitude. Incontact hole imaging especially, as well as many other imagingapplications of lines and spaces, the DOF is a limiting processperformance factor. Isolated lines and line-space patterns are alsoexpected to exhibit process window changes for modified illuminationspectra.

Examples Using Two Centerline Wavelengths

Applicants have demonstrated the feasibility of technique for wavelengthcontrol needed for this spectral engineering as shown in FIGS. 2E and2F. PZT driver 80 shown in FIG. 5A was programmed to control thewavelength of a KrF laser operating at 120 Hz to adjust each pulse byplus or minus steps of 4.0 pm. The integrated intensity values recordedon wavemeter photodiode array 180 shown in FIG. 6 are plotted in FIG.2E. This plot shows sharp peaks at pixel 450 and 618 which correspond toa centerline wavelength shaft of 4.0 pm.

Similar results are shown in FIG. 2F where the PZT driver is driven in asine wave to vary the wavelength by about 2 pm at a frequency of onehalf the laser pulse rate of 120 Hz.

Optimization of Laser Spectrum

The basic concept behind spectral engineering is to determine, usinglithography simulation, the optimal spectral shape, which will providethe maximum improvement of a given parameter. In particular examples,lithography simulations are provided for two dual-mode illuminationspectra and three three-mode illumination spectra shown in FIGS. 2G1,2G2 and 2G3. In these examples, the parameter, which is maximized is thedepth of focus, for 150 nm dense lines. From FIG. 2H 1, we see that thetwo dual-peak spectra (3 pm and 4 pm separation) are least sensitive todefocus and therefore have a maximum depth of focus. From the depth offocus changes, it appears that spectral modification (going frommonochromatic, to three to two mode illumination spectrum) providessignificant (up to 2×) improvement of DOF. From this alone, either the 3pm or 4 pm dual-mode illumination appears optimal for imaging of thesefeatures.

If we consider the tradeoff between exposure latitude (EL) and depth offocus as a function of the different illumination spectra (shown in FIG.2H 2), we may choose to use the 1.5 pm-offset 50% weighted three-modeillumination in order to prevent the reduction in exposure latitudebelow 12% at best focus. The three-mode spectrum still provides anappreciable increase in depth of focus. In addition the three-modespectrum (with 1.5 pm peak separation) provides the least amount ofcontrast loss from the monochromatic case as shown in FIG. 2H 3.

From this 150 nm dense line example, it is clear that the implementationof RELAX requires a very careful tradeoff design in order to maximizethe benefits of a subset of imaging parameters at lowest cost to otherparameters. The RELAX application will therefore be most successful incases where a single parameter limits the overall process margin(process latitude). In that case, the limiting process parameter can beimproved (relaxed) in order to improve to overall process margin formanufacturability. Optical proximity correction (OPC-resolutionenhancement technique using reticle feature corrections) can be used inconjunction with RELAX for comprehensive lithography process engineeringand maximum benefits.

The tuning of the RELAX spectral illumination, from a continuum oftheoretical choices can be done using lithography simulation and aniterative optimization algorithm. The simulation predictions also needto be verified and fine-tuned using experimental methods (such as designof experiments-DOE). Both approaches have been discussed in more detailpreviously (section IV-B 05/25/01 disclosure). FIG. 2I shows theconfluence of simulation and experiments (DOE) for either S(λ) spectrumoptimization only or for a comprehensive lithography processoptimization (variable lithography inputs) using RELAX.

Ultra Fast Wavemeter with Fast Control Algorithm Controlling PulseEnergy, Wavelength and Bandwidth

In prior art devices the feedback control of pulse energy has been on apulse-to-pulse basis, i.e., the pulse energy of each pulse is measuredquickly enough so that the resulting data can be used in the controlalgorithm to control the energy of the immediately following pulse. Fora 1,000 Hz system this means the measurement and the control for thenext pulse must take less than 1/1000 second. For a 4000 Hz systemspeeds need to be four times as fast. A technique for controlling centerwavelength and measuring wavelength and bandwidth is described in U.S.Pat. No. 5,025,455 System, and Method of Regulating the Wavelength of aLight Beam and in U.S. Pat. No. 5,978,394, Wavelength and System for anExcimer Laser. These patents are incorporated herein by reference.

Wavelength and bandwidths have been measured on a pulse to pulse basisfor every pulse, but typically the feedback control of wavelength hastaken about 7 milli-seconds because prior art techniques for controllingcenter wavelength have taken several milli-seconds. Faster control isneeded.

Preferred Embodiment for Fast Measurement and Control of Beam ParametersA preferred embodiment of the present invention is an ArF excimer lasersystem capable of operation in the range of 4,000 Hz to 6,000 Hz withvery fast measurement of laser beam parameters and very fast control ofpulse energy and center wavelength. The beam parameter measurement andcontrol for this laser is described below.

The wavemeter used in the present embodiment is very similar to the onedescribed in U.S. Pat. No. 5,978,394 and some of the description belowis extracted from that patent.

Measuring Beam Parameters

FIG. 6 shows the layouts of a preferred wavemeter unit 104, an absolutewavelength reference calibration unit 190, and a wavemeter processor197. The optical equipment in these units measure pulse energy,wavelength and bandwidth. These measurements are used with feedbackcircuits to maintain pulse energy and wavelength within desired limits.The equipment calibrates itself by reference to an atomic referencesource on the command from the laser system control processor. As shownin FIG. 6, the laser output beam intersects partially reflecting mirror170, which passes about 95.5% of the beam energy as output beam 33 andreflects about 4.5% for pulse energy, wavelength and bandwidthmeasurement.

Pulse Energy

About 4% of the reflected beam is reflected by mirror 171 to energydetector 172 which comprises a very fast photo diode 69 which is able tomeasure the energy of individual pulses occurring at the rate of 4,000pulses per second. The pulse energy for a typical ArF excimer laser isabout 5 mJ, and the output of detector 69 is fed to a computercontroller which uses a special algorithm to adjust the laser chargingvoltage to precisely control the pulse energy of future pulses based onstored pulse energy data in order to limit the variation of the energyof individual pulses and the integrated energy of bursts of pulses.

Linear Photo Diode Array

Photo diode array 180 is an integrated circuit chip comprising 1024separate photo diode integrated circuits and an associated sample andhold readout circuit as shown in FIG. 6A. The photo diodes are on a 25micrometer pitch for a total length of 25.6 mm (about one inch). Eachphoto diode is 500 micrometers long. Photo diode arrays such as this areavailable from several sources. A preferred supplier is Hamamatsu. Inour preferred embodiment, we use a Model S3903-1024Q which can be readat the rate of up to 4×10⁶ pixels/sec on a FIFO basis in which complete1024 pixel scans can be read at rates of 4,000 Hz or greater. The PDA isdesigned for 2×10⁶ pixel/sec operation but Applicants have found that itcan be over-clocked to run much faster, i.e., up to 4×10⁶ pixel/sec. Forpulse rates greater than 4,000 Hz, Applicants can use the same PDA butonly a fraction (such as 60%) of the pixels are normally read on eachscan.

Coarse Wavelength Measurement

About 4% of the beam which passes through mirror 171 is reflected bymirror 173 through slit 177 to mirror 174, to mirror 175, back to mirror174 and onto echelle grating 176. The beam is collimated by lens 178having a focal length of 458.4 mm. Light reflected from grating 176passes back through lens 178, is reflected again from mirrors 174, 175and 174 again, and then is reflected from mirror 179 and focused ontothe left side of 1024-pixel linear photo diode array 180 in the regionof pixel 600 to pixel 950 as shown in the upper part of FIG. 6B (Pixels0-599 are reserved for fine wavelength measurement and bandwidth.) Thespatial position of the beam on the photo diode array is a coarsemeasure of the relative nominal wavelength of the output beam. Forexample, as shown in FIG. 6B, light in the wavelength range of about193.350 pm would be focused on pixel 750 and its neighbors.

Calculation of Coarse Wavelength

The coarse wavelength optics in wavemeter module 120 produces arectangular image of about 0.25 mm×3 mm on the left side of photo diodearray 180. The ten or eleven illuminated photo diodes will generatesignals in proportion to the intensity of the illumination received (asindicated in FIG. 6C) and the signals are read and digitized by aprocessor in wavemeter controller 197. Using this information and aninterpolation algorithm controller 197 calculates the center position ofthe image.

This position (measured in pixels) is converted into a coarse wavelengthvalue using two calibration coefficients and assuming a linearrelationship between position and wavelength. These calibrationcoefficients are determined by reference to an atomic wavelengthreference source as described below. For example, the relationshipbetween image position and wavelength might be the following algorithm:8=(2.3 pm/pixel)P+191,625 pmwhere P=coarse image central positions.

Alternatively, additional precision could be added if desired by addinga second order term such as “+( ) P².

Fine Wavelength Measurement

About 95% of the beam which passes through mirror 173 as shown in FIG. 6is reflected off mirror 182 through lens 183 onto a diffuser (preferablya diffraction diffuser as explained in a following section entitled“Improved Etalon”) at the input to etalon assembly 184. The beam exitingetalon 184 is focused by a 458.4 mm focal length lens in the etalonassembly and produces interference fringes on the middle and right sideof linear photo diode array 180 after being reflected off two mirrors asshown in FIG. 6.

The spectrometer must measure wavelength and bandwidth substantially inreal time. Because the laser repetition rate may be 4,000 Hz to 6,000Hz, it is necessary to use algorithms which are accurate but notcomputationally intensive in order to achieve the desired performancewith economical and compact processing electronics. Calculationalalgorithm therefore preferably should use integer as opposed to floatingpoint math, and mathematical operations should preferably be computationefficient (no use of square root, sine, log, etc.).

The specific details of a preferred algorithm used in this preferredembodiment will now be described. FIG. 6D is a curve with 5 peaks asshown which represents a typical etalon fringe signal as measured bylinear photo diode array 180. The central peak is drawn lower in heightthan the others. As different wavelengths of light enter the etalon, thecentral peak will rise and fall, sometimes going to zero. This aspectrenders the central peak unsuitable for the wavelength measurements. Theother peaks will move toward or away from the central peak in responseto changes in wavelength, so the position of these peaks can be used todetermine the wavelength, while their width measures the bandwidth ofthe laser. Two regions, each labeled data window, are shown in FIG. 6D.The data windows are located so that the fringe nearest the central peakis normally used for the analysis.

However, when the wavelength changes to move the fringe too close to thecentral peak (which will cause distortion and resulting errors), thefirst peak is outside the window, but the second closest peak will beinside the window, and the software causes the processor in controlmodule 197 to use the second peak. Conversely, when the wavelengthshifts to move the current peak outside the data window away from thecentral peak the software will jump to an inner fringe within the datawindow. The data windows are also depicted on FIG. 6B.

For very fast computation of bandwidth for each pulse at repetitionrates up to the range of 4,000 Hz to 6,000 Hz a preferred embodimentuses the hardware identified in FIG. 15. The hardware includes amicroprocessor 400, Model MPC 823 supplied by Motorola with offices inPhoenix, Ariz.; a programmable logic device 402, Model EP 6016QC240supplied by Altera with offices in San Jose, Calif.; an executive anddata memory bank 404; a special very fast RAM 406 for temporary storageof photodiode array data in table form; a third 4×1024 pixel RAM memorybank 408 operating as a memory buffer; and an analog to digitalconverter 410.

As explained in U.S. Pat. Nos. 5,025,446 and U.S. Pat. No. 5,978,394,prior art devices were required to analyze a large mass of PDA datapixel intensity data representing interference fringes produced byetalon 184 an photodiode array 180 in order to determine center linewavelength and bandwidth. This was a relatively time consuming processeven with a computer processor because about 400 pixel intensity valueshad to be analyzed to look for and describe the etalon fringes for eachcalculation of wavelength and bandwidth. A preferred embodiment of thepresent invention greatly speeds up this process by providing aprocessor for finding the important fringes which operates in parallelwith the processor calculating the wavelength information.

The basic technique is to use programmable logic device 402 tocontinuously produce a fringe data table from the PDA pixel data as thepixel data are produced. Logic device 402 also identifies which of thesets of fringe data represent fringe data of interest. Then when acalculation of center wavelength and bandwidth are needed,microprocessor merely picks up the data from the identified pixels ofinterest and calculates the needed values of center wavelength andbandwidth. This process reduces the calculation time for microprocessorby about a factor of about 10.

Specific steps in the process of calculating center wavelength andbandwidth are as follows:

-   -   1) With PDA 180 clocked to operate at 2.5 MHz, PDA 180 is        directed by processor 400 to collect data at a from pixels 1 to        600 at a scan rate of 4,000 Hz and to read pixels 1 to 1028 at a        rate of 100 Hz.    -   2) The analog pixel intensity data produced by PDA 180 is        converted from analog intensity values into digital 8 bit values        (0 to 255) by analog to digital converter 410 and the digital        data are stored temporily in RAM buffer 408 as 8 bit values        representing intensity at each pixel of photodiode array 180.    -   3) Programmable logic device 402 analyzes the data passing out        of RAM buffer 408 continuously on an almost real time basis        looking for fringes, stores all the data in RAM memory 406,        identifies all fringes for each pulse, produces a table of        fringes for each pulse and stores the tables in RAM 406, and        identifies for further analysis one best set of two fringes for        each pulse. The technique used by logic device 402 is as        follows:        -   A) PLD 402 analyzes each pixel value coming through buffer            408 to determine if it exceeds an intensity threshold while            keeping track of the minimum pixel intensity value. If the            threshold is exceeded this is an indication that a fringe            peak is coming. The PLD identifies the first pixel above            threshold as the “rising edge” pixel number and saves the            minimum pixel value of the pixels preceding the “rising            edge” pixel. The intensity value of this pixel is identified            as the “minimum” of the fringe.        -   B) PLD 402 then monitors subsequent pixel intensity values            to search for the peak of the fringe. It does this by            keeping track of the highest intensity value until the            intensity drops below the threshold intensity.        -   C) When a pixel having a value below threshold is found, the            PLD identifies it as the falling edge pixel number and saves            the maximum value. The PLD then calculates the “width” of            the fringe by subtracting the rising edge pixel number from            the falling edge pixel number.        -   D) The four values of rising edge pixel number, maximum            fringe intensity, minimum fringe intensity and width of the            fringe are stored in the circular table of fringes section            of RAM memory bank 406. Data representing up to 15 fringes            can be stored for each pulse although most pulses only            produce 2 to 5 fringes in the two windows.        -   E) PLD 402 also is programmed to identify with respect to            each pulse the “best” two fringes for each pulse. It does            this by identifying the last fringe completely within the 0            to 199 window and the first fringe completely within the 400            to 599 window.

The total time required after a pulse for (1) the collection of thepixel data, and (2) the formation of the circular table of fringes forthe pulse is only about 200 micro seconds. The principal time savingadvantages of this technique is that the search for fringes is occurringas the fringe data is being read out, digitized and stored. Once the twobest fringes are identified for a particular pulse, microprocessor 400secures the raw pixel data in the region of the two fringes from RAMmemory bank 406 and calculates from that data the bandwidth and centerwavelength. The calculation is as follows:

Typical shape of the etalon fringes are shown in FIG. 6D. Based on theprior work of PLD 402 the fringe having a maximum at about pixel 180 andthe fringe having a maximum at about pixel 450 will be identified tomicroprocessor 400. The pixel data surrounding these two maxima areanalyzed by microprocessor 400 to define the shape and location of thefringe. This is done as follows:

A half maximum value is determined by subtracting the fringe minimumfrom the fringe maximum dividing the difference by 2 and adding theresult to the fringe minimum. For each rising edge and each falling edgeof the two fringes the two pixels having values of closest above andclosest below the half maximum value. Microprocessor then extrapolatesbetween the two pixel values in each case to define the end points of D1and D2 as shown in FIG. 6D with a precision of {fraction (1/32)} pixel.From these values the inner diameter D1 and the outer diameter D2 of thecircular fringe are determined.

Fine Wavelength Calculation

The fine wavelength calculation is made using the course wavelengthmeasured value and the measured values of D1 and D2.

The basic equation for wavelength is:λ=(2*n*d/m)cos(R/f)  (1)where

-   -   λ is the wavelength, in picometers,    -   n is the internal index of refraction of the etalon, about        1.0003,    -   d is the etalon spacing, about 1542 um for KrF lasers and about        934 :m for ArF lasers, controlled to +/−1 um,    -   m is the order, the integral number of wavelengths at the fringe        peak, about 12440,    -   R is the fringe radius, 130 to 280 PDA pixels, a pixel being 25        microns,    -   f is the focal distance from the lens to the PDA plane.

Expanding the cos term and discarding high order terms that arenegligibly small yields:λ=(2*n*d/m)[1−(½)(R/f)²]  (2)

Restating the equation in terms of diameter D=2*R yields:λ=(2*n*d/m)[1−(⅛)(D/f)²]  (3)

The wavemeter's principal task is to calculate k from D. This requiresknowing f, n, d and m. Since n and d are both intrinsic to the etalon wecombine them into a single calibration constant named ND. We consider fto be another calibration constant named FD with units of pixels tomatch the units of D for a pure ratio. The integer order m variesdepending on the wavelength and which fringe pair we choose. m isdetermined using the coarse fringe wavelength, which is sufficientlyaccurate for the purpose.

A couple of nice things about these equations is that all the bignumbers are positive values. The WCM's microcontroller is capable ofcalculating this while maintaining nearly 32 bits of precision. We referto the bracketed terms as FRAC.FRAC=[1−(⅛)(D/FD)²]  (4)

Internally FRAC is represented as an unsigned 32 bit value with itsradix point to the left of the most significant bit. FRAC is always justslightly less than one, so we get maximal precision there. FRAC rangesfrom [1-120E-6] to [1-25E-6] for D range of {560˜260} pixels.

When the ND calibration is entered, the wavemeter calculates an internalunsigned 64 bit value named 2ND=2*ND with internal wavelength units offemtometers (fm)=10⁻¹⁵ meter=0.001 pm. Internally we represent thewavelength λ as FWL for the fine wavelength, also in fm units. Restatingthe equation in terms of these variables:FWL=FRAC*2ND/m  (5)

The arithmetic handles the radix point shift in FRAC yielding FWL infin. We solve for m by shuffling the equation and plugging in the knowncoarse wavelength named CWL, also in fm units:m=nearest integer (FRAC*2ND/CWL)  (6)

Taking the nearest integer is equivalent to adding or subtracting FSRsin the old scheme until the nearest fine wavelength to the coarsewavelength was reached. Calculate wavelength by solving equation (4)then equation (6) then equation (5). We calculate WL separately for theinner and outer diameters. The average is the line center wavelength,the difference is the linewidth.

Bandwidth Calculation

The bandwidth of the laser is computed as (8₂−8₁)/2. A fixed correctionfactor is applied to account for the intrinsic width of the etalon peakadding to the true laser bandwidth. Mathematically, a deconvolutionalgorithm is the formalism for removing the etalon intrinsic width fromthe measured width, but this would be far too computation-intensive, soa fixed correction )8, is subtracted, which provides sufficientaccuracy. Therefore, the bandwidth is:${{)\lambda} = {\left( \frac{D_{2} - D_{1}}{2} \right) - {\text{)}8}}},$)8, depends on both the etalon specifications and the true laserbandwidth. It typically lies in the range of 0.1-1 pm for theapplication described here.

Improved Etalon

This embodiment utilizes an improved etalon. Conventional etalonmounting schemes typically employ an elastomer to mount the opticalelements to the surrounding structure, to constrain the position of theelements but minimize forces applied to the elements. A compoundcommonly used for this is room-temperature vulcanizing silicone (RTV).However, various organic vapors emitted from these elastomers candeposit onto the optical surfaces, degrading their performance. In orderto prolong etalon performance lifetime, it is desirable to mount theetalon in a sealed enclosure that does not contain any elastomercompounds.

A preferred embodiment includes an improved etalon assembly shown at 184in FIGS. 6 and 6E. The fused silica etalon 79 shown in FIG. 6G itself iscomprised of a top plate 80 having a flange 81 and a lower plate 82,both plates being comprised of premium grade fused silica. The etalon isdesigned to produce fringes having free spectral range of 20.00 pm at193.35 nm when surrounded by gas with an index of refraction of 1.0003and a finesse equal to or greater than 25. Three fused silica spacers 83with ultra low thermal expansion separate the plates and are 934micrometer ∀1 micrometer thick. These hold the etalon together byoptical contact using a technique well known in the optics manufacturingart. The reflectance of the inside surfaces of the etalon are each about88 percent and the outside surfaces are anti-reflection coated. Thetransmission of the etalon is about 50 percent.

The etalon 79 is held in place in aluminum housing 84 only by gravityand three low force springs 86 pressing the flange against three padsnot shown but positioned on 120 degree centers under the bottom edge offlange 81 at the radial location indicated by leader 85. A clearance ofonly 0.004 inch along the top edge of flange 81 at 87 assures that theetalon will remain approximately in its proper position. This closetolerance fit also ensures that if any shock or impulse is transferredto the etalon system through the mounting, the relative velocitiesbetween the optical components and the housing contact points will bekept to a minimum. Other optical components of etalon assembly 184include diffuser 88, window 89 and focusing lens 90 having a focallength of 458.4 mm.

The diffuser 88 may be a standard prior art diffuser commonly usedup-stream of an etalon to produce a great variety of incident anglesneeded for the proper operation of the etalon. A problem with prior artdiffusers is that about 90 percent of the light passing through thediffuser is not at a useful angle and consequently is not focused on thephoto diode array. This wasted light, however, adds to the heating ofthe optical system and can contribute to degradation of opticalsurfaces. In a much preferred embodiment, a diffractive lens array isused as the diffuser 88. With this type of diffuser, a pattern isproduced in the diffractive lens array which scatters the lightthoroughly but only within an angle of about 5 degrees. The result isthat about 90 percent of the light falling on the etalon is incident atuseful angles and a much greater portion of the light incident on theetalon is ultimately detected by the photo diode array. The result isthe light incident on the etalon can be greatly reduced which greatlyincreases optical component life. Applicants estimate that the incidentlight can be reduced to less than 5% or 10% of prior art values withequivalent light on the photo diode array.

Better Collimation with Diffractive Diffuser

FIG. 6H shows features of a preferred embodiment providing even furtherreduction of light intensity passing through the etalon. This embodimentis similar to the embodiment discussed above. The sample beam frommirror 182 (approximately 15mm×3 mm) passes upward through condensinglens 400 and is then re-collimated by lens 402. The beam nowcolliminated and reduced in dimension to about 5 mm×1 mm passes throughetalon housing window 404 and then passes through a diffractivediffusing element 406 which in this case (for an ArF laser) is adiffractive diffusing element provided by Mems Optical, Inc. withoffices in Huntsville, Ala. The element is part number D023-193 whichconverts substantially all 193 nm light in any incoming collimated beamof any cross sectional configuration into a beam expanding in a firstdirection at 2E and in a second direction perpendicular to the firstdirection at 4E. Lens 410 then Afocuses≅the expanding beam onto arectangular pattern covering photodiode array 180 shown in FIG. 6. Theactive area of the photo diode array is about 0.5 mm wide and 25.6 mmlong and the spot pattern formed by lens 410 is about 15 mm×30 mm.Diffractive diffusing element thoroughly mixes the spatial components ofthe beam but maintains substantially all of the beam energy within the2E and 4E limits so that the light passing through the etalon can besubstantially reduced and efficiently utilized. The reader shouldrecognize that further reductions in beam energy passing through theetalon could be realized by reducing the spot pattern in the shortdimension of the photo diode array. However, further reductions to lessthan 15 mm will make optical alignment more difficult. Therefore, thedesigner should consider the spot pattern size to be a trade-off issue.

In another system designed for a KrF laser operating at about 248.327 nma similar design is provided with adjustments for wavelength. In thisembodiment lens 400 has a focal length of about 50 mm. (The lens isMelles Griot Corporation part number OILQP001.) Collimating lens 402 hasa focal length of −20 mm (EVI Laser Corporation part numberPLCC-10.0-10.3-UV). The diffractive diffusing element 406 is MemsOptical Corporation part number D023-248. In this embodiment and in theArF embodiment, the spacing between the two lenses can be properlypositioned with spacer 416. Applicants estimate that the energy of thebeam passing through the etalon with the laser operating at 2000 Hz isabout 10 mw and is not sufficient to cause significant thermal problemsin the etalon.

In other preferred embodiments, the beam could be allowed to come to afocus between lenses 400 and 402. Appropriate lenses would in this casebe chosen using well known optical techniques.

Feedback Control of Pulse Energy and Wavelength

Based on the measurement of pulse energy of each pulse as describedabove, the pulse energy of subsequent pulses are controlled to maintaindesired pulse energies and also desired total integrated dose of aspecified number of pulses all as described in U.S. Pat. No. 6,005,879,Pulse Energy Control for Excimer Laser which is incorporated byreference herein.

Wavelength of the laser may be controlled in a feedback arrangementusing measured values of wavelengths and techniques known in the priorart such as those techniques described in U.S. Pat. No. 5,978,394,Wavelength System for an Excimer Laser also incorporated herein byreference. Applicants have recently developed techniques for wavelengthtuning which utilize a piezoelectric driver to provide extremely fastmovement of tuning mirror. Some of these techniques are described inUnited States Patent Application Serial No. 608,543, Bandwidth ControlTechnique for a Laser, filed Jun. 30, 2000 which is incorporated hereinby reference. FIGS. 8A and 8B are extracted from that application andshow the principal elements of this technique. A piezoelectric stack isused for very fast mirror adjustment and larger slower adjustments areprovided by a prior art stepper motor operating a lever arm. Thepiezoelectric stack adjusts the position of the fulcrum of the leverarm.

New LNP with Combination PZT-Stepper Motor Driven Tuning Mirror DetailDesign with Piezoelectric Drive

FIG. 8 is a block diagram showing features of the laser system which areimportant for controlling the wavelength and pulse energy of the outputlaser beam. Shown are a line narrowing module 15K which contains a threeprism beam expander, a tuning mirror 14 and a grating. Wavemeter 104monitors the output beam wavelength and provides a feedback signal toLNP processor 106 which controls the position of tuning mirror 14 byoperation of a stepper motor and a PZT stack as described below.Operational wavelengths can be selected by laser controller 102. Pulseenergy is also measured in wavemeter 104 which provides a signal used bycontroller 102 to control pulse energy in a feedback arrangement asdescribed above. FIG. 8A is a block diagram showing PZT stack 80,stepper motor 82, mirror 14 and mirror mount 86.

FIG. 8B 1 is a drawing showing detail features of a preferred embodimentof the present invention. Large changes in the position of mirror 14 areproduced by stepper motor through a 26.5 to 1 lever arm 84. In this casea diamond pad 41 at the end of piezoelectric drive 80 is provided tocontact spherical tooling ball at the fulcrum of lever arm 84. Thecontact between the top of lever arm 84 and mirror mount 86 is providedwith a cylindrical dowel pin on the lever arm and four spherical ballbearings mounted (only two of which are shown) on the mirror mount asshown at 85. Piezoelectric drive 80 is mounted on the LNP frame withpiezoelectric mount 80A and the stepper motor is mounted to the framewith stepper motor mount 82A. Mirror 14 is mounted in mirror mount 86with a three point mount using three aluminum spheres, only one of whichare shown in FIG. 8B 1. Three springs 14A apply the compressive force tohold the mirror against the spheres.

FIG. 8B 2 is a preferred embodiment slightly different from the oneshown in FIG. 8B 1. This embodiment includes a bellows 87 to isolate thepiezoelectric drive from the environment inside the LNP. This isolationprevents UV damage to the piezoelectric element and avoid possiblecontamination caused by out-gassing from the piezoelectric materials.

Test Results

FIG. 8C shows actual test data from a laser fitted with the FIG. 8B 2embodiment. The graph is a plot of the deviation from target wavelengthof the average of 30 pulse windows. The deviation is reduced from about0.05 pm to about 0.005 pm.

This embodiment is a major speed up as compared to the stepper motordrive system described above but not quite fast enough forpulse-to-pulse adjustment. Earlier methods of mirror positioningrequired about 7 ms to move mirror 14, making pulse-to-pulse wavelengthcorrection at 2000 Hz out of the question. In that earlier technique, alever arm pivoted about a pivot axis to produce a 1 to 26.5 reduction inthe mirror movement compared to the stepper position movement. The priorart stepper has a total travel of ½ inch (12.7 mm) and 6000 steps sothat each step is a distance of about 2 microns. With the 1-26.5reduction, one step moves the mirror about 75 nm which typically changesthe wavelength of the laser wavelength about 0.1 pm. In the fast actingtechnique shown in FIG. 12A, a piezo stack 80 has been added at thepivot position of the lever arm. A preferred piezo stack is ModelP-840.10 supplied by Physik Instrumente GmbH with offices in Waldbronn,Germany.

This stack will produce linear adjustment of about 3.0 microns with adrive voltage change of 20 volts. This range is equivalent to about ∀ 20steps of the stepper motor.

The stack responds to a control signal within less than 1 microsecondand the system can easily respond to updated signals at a frequency of4000 Hz. In a preferred embodiment the control for each pulse at 4000 Hzpulse rate is based not on the previous pulse but the pulse prior to theprevious pulse to allow plenty of time for the wavelength calculation.However, this embodiment provides a factor of 7 improvement over theprior art design with a 7 millisecond latency. Therefore, much fasterfeedback control can be provided. One preferred feedback controlalgorithm is described in FIG. 8D. In this algorithm the wavelength ismeasured for each pulse and an average wavelength for the last four andlast two pulses is calculated. If either of the averages deviate fromthe target wavelength by less than 0.02 pm, no adjustment is made. Ifboth deviate more than 0.02 pm from the target, an adjustment is made tothe mirror assembly by piezoelectric stack 80 to provide a wavelengthcorrection. Which of the two averages is used is determined by how muchtime had elapsed since the last adjustment. The piezoelectric stack ismaintained within its control range by stepping the stepper motor as thestack approaches 30 and 70 percent of its range (or to provide moreavailable range, 45 and 55 percent could be used instead of the 30 and70 percent range values). Since the stepper motor requires about 7 ms tocomplete a step, the algorithm may make several piezo adjustments duringa stepper motor step.

Issues Involved in Applying Periodic Inputs for Bandwidth Tuning(Mathematical Analysis)

Applicants have investigated methods of controlling the PZT to achievedesired broader bandwidth. The following is an example of analysis doneby Applicants to achieve these results. The problem is to apply periodicvoltages to PZT 80 which when filtered by dynamics of the tuning mirrorsystem results in bandwidths having the desired values.

A method is needed to monitor the error between the desired and actualwavelength values and make adjustments to the applied voltage in realtime. Such a method would detect the error caused by non-linearities orimperfect modeling of the system and could correct for them. It wouldalso follow any drifting dynamics and maintain optimal periodic commandfollowing.

Described below are several different methods for determining andadjusting the applied voltage, u, to generate the desired wavelengthpattern, r, in real time.

The first approach is to observe the error, e, for a single period ofthe desired pattern, r, and then compute an adjustment to the appliedvoltage, u, which will tend to reduce the error. The appropriate law canbe found by first expressing the error, e, as the difference between theactual and desired patterns.e=r−y  (1)

The actual wavelength, y, is related to the periodic input, u, by theequation: $\begin{matrix}{{y(t)} = {\sum\limits_{\tau = 0}^{N - 1}{{h_{c}\left( {t - \tau} \right)}{u(t)}}}} & (2)\end{matrix}$where N is the period of the command signal, h_(c) is the cyclic pulseresponse of the voltage to wavelength system. The cyclic pulse responseis related to the pulse response by the equation: $\begin{matrix}{{h_{c}(t)} = {\sum\limits_{\tau = 0}^{\infty}{h\left( {t + {N\quad\tau}} \right)}}} & (3)\end{matrix}$

Define an error function which is the sum of squares of the error:$\begin{matrix}{J \equiv {\sum\limits_{t = 0}^{N - 1}{e^{2}(t)}}} & (4)\end{matrix}$

The derivative of this error function with respect to the value of theperiodic control voltage at any instant in time, u(t) is found to be:$\begin{matrix}{\frac{\partial J}{u(t)} = {{- 2}{\sum\limits_{\tau = 0}^{N - 1}{{e(\tau)}{h_{c}\left( {\tau - t} \right)}}}}} & (5)\end{matrix}$

The control law is then simply to update all of the values of thecontrol signal, u, according to the equation: $\begin{matrix}{{u(t)}->{{u(t)} + {\mu{\sum\limits_{\tau = 0}^{N - 1}{{e(\tau)}{h_{c}\left( {\tau - t} \right)}}}}}} & (6)\end{matrix}$where the parameter, μ is adjusted to trade convergence speed forstability and noise insensitivity. If the value of μ is chosen smallenough, this control law is guaranteed to converge to the optimalcancellation waveform.

A refinement of this method is to limit the number of degrees of freedomin the control signal, u. This might be done to limit the bandwidth ofthe signal being put into the actuator, or it might be used to improvethe convergence time of the algorithm. The number of degrees of freedomcan be reduced by expressing u as a some of basis functions, φ:$\begin{matrix}{{u(t)} = {\sum\limits_{i = 0}^{m - 1}{{\phi_{i}(t)}q_{i}}}} & (7)\end{matrix}$

Typical values for the basis functions might be sine waves correspondingto the first few harmonics of the fundamental frequency. This would ineffect limit the bandwidth of the applied signal, u. Taking thederivatives of J with respect to q_(i) gives yields a control law foradjusting the q_(i)'s every cycle: $\begin{matrix}{\frac{\partial J}{\partial q_{i}} = {{- 2}{\sum\limits_{t = 0}^{N - 1}{{e(t)}{\sum\limits_{\tau = 0}^{N - 1}{{h_{c}\left( {t - \tau} \right)}{\phi_{i}(\tau)}}}}}}} & (8) \\{q_{i}->{q_{i} + {\mu{\sum\limits_{t = 0}^{N - 1}{{e(t)}{\sum\limits_{\tau = 0}^{N - 1}{{h_{c}\left( {t - \tau} \right)}{\phi_{i}(\tau)}}}}}}}} & (9)\end{matrix}$

An improvement can be made to the algorithm by adjusting each componentof the correction signal, u(t), just before it is applied. The data forthe adjustment is the error signal from the previous N samples. Equation6 can be rewritten as follows: $\begin{matrix}\begin{matrix}{{u(t)} = {{u\left( {t - N} \right)} + {\mu{\sum\limits_{\tau = 0}^{N - 1}{{e\left( {\tau + t - N} \right)}{h_{c}\left( {\tau - N} \right)}}}}}} \\{= {{u\left( {t - N} \right)} + {\mu{\sum\limits_{\tau = 0}^{N - 1}{{h_{c}(t)}{e\left( {\tau - N + t} \right)}}}}}}\end{matrix} & (10)\end{matrix}$

The first line of the equation results from the fact that the controlsignal exactly N cycles previously corresponds to the control signalcurrently being adjusted. The second line follows by a change ofvariable in the summation. Taking the z-transform of Equation 10:$\begin{matrix}{{u(z)} = {{z^{- N}{u(z)}} + {\mu{\sum\limits_{\tau = 0}^{N - 1}{{h_{c}(t)}{e(z)}z^{\tau - N}}}}}} & (11)\end{matrix}$

The ratio of u(z) and e(z) yield an LTI filter which implements theadaptation law on a sample by sample basis. $\begin{matrix}{{K(z)} = {\frac{u(z)}{e(z)} = {µ\frac{\sum\limits_{\tau = 0}^{N - 1}\quad{{h_{c}(\tau)}z^{\tau - N}}}{1 - z^{- N}}}}} & (12)\end{matrix}$

Note that there are N controller poles equally spaced around the unitcircle. This compensator will have infinite gain at each harmonic of thefundamental frequency. This control law can be refined by using apartial fraction expansion: $\begin{matrix}{{K(z)} = {{\sum\limits_{k = 0}^{N - 1}{\frac{r_{k}}{z - z_{k}}\quad z_{k}}} = {\mathbb{e}}^{j\quad 2\pi\quad{k/N}}}} & (13)\end{matrix}$

The residues, r_(k), can be found from the following Equation:$\begin{matrix}{r_{k} = {\frac{\sum\limits_{\tau = 0}^{N - 1}\quad{{h_{c}(\tau)}z^{\tau - N}}}{\prod\limits_{i \neq k}\quad\left( {z_{k} - z_{i}} \right)} = {\frac{\sum\limits_{\tau = 0}^{N - 1}\quad{{h_{c}(\tau)}z_{k}^{\tau}}}{\prod\limits_{i \neq k}\quad\left( {z_{k} - z_{i}} \right)} = \frac{G\left( z_{k}^{- 1} \right)}{\prod\limits_{i \neq k}\quad\left( {z_{k} - z_{i}} \right)}}}} & (14)\end{matrix}$

The last equality of this equation follows directly from Equation 3 andthe definition of the z-transform. The term in the denominator can befound by applying L'Hopital's rule: $\begin{matrix}{{\prod\limits_{i \neq k}\quad\left( {z_{k} - z_{i}} \right)} = {{\lim\limits_{z->z_{k}}\frac{\left( {z^{N} - 1} \right)}{z - z_{k}}} = {{\lim\limits_{z->z_{k}}\frac{{Nz}^{N - 1}}{1}} = {{Nz}_{k}^{N - 1} = {Nz}_{k}^{- 1}}}}} & (15)\end{matrix}$

Thus the residues are given by: $\begin{matrix}{r_{k} = \frac{G\left( z_{k}^{- 1} \right)}{N\quad z_{k}^{- 1}}} & (16)\end{matrix}$

And the compensator is therefore: $\begin{matrix}{{K(z)} = {µ{\sum\limits_{k = 0}^{N - 1}\quad\frac{z_{k}{G\left( z_{k}^{- 1} \right)}}{N\left( {z - z_{k}} \right)}}}} & (17)\end{matrix}$

FIG. 9A shows the loop transfer function for the compensator in Equation17 applied to a model based on measurements made from applied R_(max)voltage to wavelength for an LNP from a 7000A laser. Note that thetransfer function has infinite gain at DC, the fundamental frequency,and all of its harmonics. This filter will achieve perfect following ofthe periodic command, r, provided that it is closed loop stable. ANyquist plot for the transfer function with a small amount of dampingconfirms that the filter is closed loop stable.

FIG. 9B shows a simulation of this algorithm. The simulation employed amodel based on measurements taken from a 4000 Hz Arf excimer laser. Thelight line in the figure represents a wavelength pattern which willyield a desired spectrum when integrated over a slit width of 30 pulses.The heavy line represents the actual wavelength output by the laser. Thesimulation was started with the input signal to actuator, u(t), setequal to zero for all 30 pulses. The simulation shows that within 250ms, nearly perfect following of the commanded input has been achieved.

An additional refinement can be made to the control law analogous tousing the basis functions of Equation 7. Instead of allowing thecontroller to cancel the signal at all harmonics, we can limit thecancellation to just the first few harmonics by not including all of theterms in Equation 17. $\begin{matrix}{{K(z)} = {{µ{\sum\limits_{k = {- n}}^{n}\quad{\frac{z_{k}{G\left( z_{k}^{- 1} \right)}}{N\left( {z - z_{k}} \right)}\quad z_{k}}}} = {\mathbb{e}}^{{j2\pi}\quad{k/N}}}} & (18)\end{matrix}$

An example of the loop transfer function which results for n=3 is shownin FIG. 9C. Infinite gain is achieved only at DC and the first threeharmonics. Again, a Nyquist plot (not shown) reveals that stability isstill being maximized. Application of this control law would yieldoptimal matching of the desired wavelength pattern r, subject to theconstraint that the control signal is band limited.

FIG. 9D shows the simulation using the FIG. 9C transfer function. Asbefore the light line represents the desired pattern and the heavy linerepresents the actual wavelength of the laser. Note that while thecancellation is no longer perfect, convergence was achieved in only 40ms, an 84% reduction over the full order case.

Techniques for Bandwidth Tuning Using PZT

For reasons discussed in the previous section, care must be exercised inapplying controls to the PZT in order to vary the center line wavelengthto simulate a broader bandwidth for a series of pulses. This is becausethe response of the PZT controlled tuning mirror system is not linearfor periodic signal inputs. The apparent gain of the PZT deviceincreases with higher voltage inputs. Further, even if the system wereperfectly linear, the dynamics might vary over time. A system initiallyproducing the desired wavelength and bandwidth values would eventuallyproduce distorted values as the dynamics drifted away from the designpoint. In fact, substantial resonances are present in the typical systemat high frequency input signals. FIGS. 9A and 9C indicate the generalshapes of damping functions needed to compensate for resonances atfrequencies higher than about 50 Hz.

Other Approaches

The PZT driver can be programmed to simulate virtually any desiredspectrum. Some of the techniques for precisely controlling thewavelength with the PZT driving the tuning mirror 14 are described inU.S. patent application Ser. No. ______ filed simultaneously with thisapplication and incorporated by reference herein. For example, FIG. 10Ashows a desired Gaussian spectrum with FWHM of 3.3 pm and a simulatedfit for a 30-pulse window of pulses having a FWHM of 0.8 pm. FIG. 10Bshows a proposed sequence of pulses for the 30-pulse window in which thecenter line wavelength follows a generally sine pattern. FIG. 10Ccompares the frequency content of a smooth wavelength sequence such asthe FIG. 10B with a random sequence. FIGS. 10D and 10E show the effectof 133 Hz sine pattern and a 30-pulse window and a 40 Hz sine with a100-pulse window. FIGS. 10F and 10G show how to produce a flat-topspectrum.

The reader should understand that rapid changes in mirror positionresult in substantial non-linearities. One solution could be tosyncronize mirror motion with pulse repetition rate such as shown inFIG. 10H and FIG. 101I.

While particular embodiments of the present invention have been shownand described, it will be obvious to those skilled in the art thatchanges and modifications may be made without departing from thisinvention in its broader aspects. For example, partially line narrowedlasers where the bandwidth is line narrowed with a plurality of prismsand the beam is reflected with a tuning mirror. This technique wouldinvolve dithering the tuning mirror. The peak separation could vary fromthe examples shown. Normally, however, the peaks would be offset by atleast 0.5 pm. In lithography, bursts of pulses normally contain about 20to 400 pulses. Most lithography units now operate at 1000 Hz or greater.It should also be recognized that these dithering techniques helps toeliminate coherence problems. Instead of dithering the mirror toincrease the effective bandwidth, the grating could be dithered with adither pattern chosen to produce an effective larger bandwidth ordesired effective spectrum. Therefore, the appended claims are toencompass within their scope all such changes and modifications as fallwithin the true spirit and scope of this invention.

1. A process for providing lithographic exposures utilizing a linenarrowed bas discharge laser, comprising the steps of: A. modeling witha computer program lithographic parameters to determine a desired laserspectrum needed to produce a desired lithographic result, b. utilizing afast responding tuning mechanism to adjust center wavelength of laserpulses in a burst of pulses to achieve an integrated spectrum for theburst of pulses approximating the desired laser spectrum.
 2. A processas in claim 1 wherein said burst of pulses are a number of pulse withinthe range of about 20 to 400 pulses.
 3. A process as in claim 1 whereinsaid burst of pulses are produced as a repetition rate in excess of 1000pulses per second.
 4. A process as in claim 3 wherein a wavelengthspectrum is measured for each pulse.
 5. A process as in claim 4 whereinwavelength measured for each pulse is used to control wavelength of oneor more subsequent pulses.
 6. A process as in claim 1 wherein saiddesired laser spectrum comprises two or more separate peaks.
 7. Aprocess as in claim 6 wherein said two or more peaks are separated by atleast 0.5 picometer.
 8. A process as in claim 6 wherein said desiredspectrum comprises three separate peaks.
 9. A process for producingeffective bandwidths of a pulse laser beam of a narrow band electricdischarge laser having a line narrowing unit comprising a grating and afast tuning mechanism, said process comprising the steps of: A)monitoring said laser beam to determine bandwidth of individual pulseslaser pulses, B) periodically adjusting the tuning mechanism during aseries of pulses so that the wavelengths of some pulses in said seriesof pulses are slightly longer than a target wavelength and thewavelengths of some pulses in said series of pulses are slightly shorterthan the target wavelength in order to produce for the series of pulsesan average spectrum centered approximately at the target wavelength withaverage spectral deviation from the target wavelength approximatelyequal to a desired deviation.
 10. A process as in claim 9 wherein saidline narrowing unit comprises a piezoelectric drive unit.
 11. A processas in claim 10 wherein said line narrowing unit comprises a tuningmirror driven by said piezoelectric drive unit.
 12. A process as inclaim 9 wherein the bandwidths of individual pulses are determined bydetermining a slit function of a spectrometer, determining a raw dataspectrum, for said laser convolving the raw data spectrum with the slitfunction to produce a forward convolved spectrum determining width forthe forward convolved spectrum W_(FC) and a width of the raw dataspectrum, W_(R) computing an estimate of the width of the true spectrumW_(T) by a formula equivalent to:W _(T) =W _(R)−(W _(FC) −W _(R)).